Dislocation line-tension estimate ($T_{\ell }\sim G{b}^2$)

A curved dislocation can be approximated as a line with tension $T_{\ell }$ of order $G{b}^2$. The coefficient depends on elastic constants, character and logarithmic length scales. The simple estimate $T_{\ell }\simeq G{b}^2/2$ gives a pinning bypass stress $Gb/\ell$ for a semicircular segment of free span $\ell$.